(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For many differential equations, the easiest way to find inflection points is to use the differential equation rather than the solution itself. To do this, we can compute [tex]y''[/tex] by differentiating [tex]y'[/tex], remembering to use the chain rule wherever [tex]y[/tex] occurs. Next, we can substitute for [tex]y'[/tex] by using the differential equation and setting [tex]y' = 0[/tex]. Then we can solve for [tex]y[/tex] to find the inflection points. (Keep in mind here that solving for [tex]y[/tex] can also produce some equilibrium solutions, which may not be inflection points!)

Use the technique described above to find the inflection point for the solutions of the differential equation

[tex]y'=r(1-\frac{y}{L})y[/tex]

your answer may contain [tex]L[/tex] and [tex]r[/tex]

[tex]y = ?[/tex]

3. The attempt at a solution

I differentiated the given equation and set it equal to zero, then I solved it for y. My answer was Lr/4 but this is wrong according to webworks.

The equation I got when I differentiated [tex]y'=r(1-\frac{y}{L})y[/tex] was [tex]y'' = r-((4y)/L)[/tex]

i know the answer is [tex]L/2[/tex] but I dont know how to get there.

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# Homework Help: Finding inflection points

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